Automated real-time particle characterization and three-dimensional velocimetry with holographic video microscopy

ABSTRACT

An in-line holographic microscope can be used to analyze on a frame-by-frame basis a video stream to track individual colloidal particles&#39; three-dimensional motions. The system and method can provide real time nanometer resolution, and simultaneously measure particle sizes and refractive indexes. Through a combination of applying a combination of Lorenz-Mie analysis with selected hardware and software methods, this analysis can be carried out in near real time. An efficient particle identification methodology automates initial position estimation with sufficient accuracy to enable unattended holographic tracking and characterization.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a Divisional of U.S. application Ser. No.13/254,403, filed Feb. 15, 2012, which is a National Stage ofPCT/US2010/021045, filed Jan. 14, 2010, incorporated herein by referencein their entirety, which claims priority from Provisional ApplicationU.S. Application 61/145,402, filed Jan. 16, 2009, incorporated herein byreference in its entirety and which claims priority from ProvisionalApplication U.S. Application 61/171,199, filed Apr. 21, 2009,incorporated herein by reference in its entirety.

This work was supported by the National Science Foundation through GrantNumber DMR-0606415. The U.S. Government has certain rights pursuant tothis National Science Foundation Grant.

BACKGROUND OF THE INVENTION

This characterization of colloidal particles, particularly spheres, isan important and pervasive issue in many aspects of industrial chemical,physical and biomedical applications. A variety of importantfunctionalities are being sought to perform various characterizationsincluding 1) bead based molecular binding assays, 2) flow fieldmeasurements, 3) automated particle image detection in holograms, and 4)real time analysis of particle features. For example, coherentillumination traditionally has not been used widely for particle imagevelocimetry because the resulting holographic images can be difficult tointerpret quantitatively. Consequently, measurements of fluoroscenceyield has been used to carry out bead based molecular binding assaysusing holographic imaging in one color. However, such methods requirefluorescent labeling with conventional assays requiring tens ofthousands of beads to eliminate artifacts to non-specific fluorosporebinding and unintentional bleaching. It has been recently demonstratedthat holographic video microscopy images of colloidal particles can beused to locate the particles' centers in three dimensions, even whenparticles occlude each other along the optical axis. Earlierdemonstrations using phenomenological models for the observed scatteringpatterns achieved tracking resolution comparable to that attained withconventional particle imaging methods. The principal benefit of coherentillumination in these studies was the greatly extended working distanceand depth of focus compared with conventional imaging methods. However,these methods are inefficient, do not allow any real time analysis to beperformed and cannot even perform a number of characterizations (such asthe four listed above). Consequently, characterizations mentioned abovehave not been possible heretofore, have not been commercially feasibleor problems remain without apparent solution.

SUMMARY OF THE INVENTION

In therefore an object of the invention to provide a variety ofcharacterization methods and systems for analysis of colloidalparticles, such as spheres, in an automated, real-time manner usingholographic video microscopy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows an example of an in-line holographic video microscope;FIG. 1B is a magnified portion of FIG. 1A around the sample; aninterference pattern is shown in FIG. 1C(1) and FIG. 1C(2) shows a fitof FIG. 1C(1) to predictions of Lorenz-Mie theory to obtain variousmeasurements;

FIG. 2 shows processing speed and relative error in z_(p) for fits,performed in accordance with the invention, to measured holographicimages of a 2.2 μm diameter silica sphere using a one-dimensionallook-up-table (squares) and single-precision GPU-accelerated fits(circles); the inset image shows a typical 201×201 pixel hologram anderrors are computed relative to the double precision result obtained ona single-thread of the CPU (central processing unit), whose processingrate is indicated by the dashed line and the smooth curve is a guide tothe eye;

FIGS. 3A and 3B are, respectively, an original and transformedholographic images of three colloidal spheres; superimposed linesegments in FIG. 3A indicate the “votes” cast by three representativepixels and intensity in FIG. 3B is scaled by the number of votes, withblack representing 0 and white representing 800 votes and superimposedsurface plots illustrate the middle sphere's transformation (Scale barindicates 10 μm.);

FIG. 4 show the root-mean-square error in the hologram estimated for a1.5 μm diameter silica sphere in water as a function of the error inradius, Δa_(p), refractive index, Δn_(p), and axial position Δz_(p),where the curve indicates the path of minimum error parameterized byΔz_(p);

FIG. 5A shows holographic particle image velocimetry measured throughdimensional trajectories of 500 colloidal spheres traveling down amicrofluidic channel in a pressure driven flow with each sphererepresenting the particle position in one field of a holographicsnapshot and features from field sequences are linked into trajectorieswith gray scale showing a range of particle measured speeds; FIG. 5Bshows a Poiseuille flow profile along the vertical direction attainedfrom FIG. 5A data with particles excluded from the shaded region byinteractions with upper and lower glass walls of the channel (the dashedcurve is a fit to the anticipated parabolic flow profile);

FIG. 6A(1) is a distribution of streaming particles as a function ofindex of refraction and observed sizes for a commercial polystyrenespherical particle continuing sample in water; FIG. 6A(2) is a 2D crosssection from FIG. 6A(1) for the particle size and FIG. 6A(3) for indexof refraction, both being at the mean value of the other parameter;FIGS. 6B(1) and 6B(2) show trajectory averaged radius and refractiveindex as a function of mean speed;

FIG. 7A shows detection of avidin binding to biotinylated polystyrenespheres with light circles the probability distribution for measuredparticle radius in stock spheres with dark circles having acorresponding distribution for a sample of the sphere after incubationwith neutravidin (dashed curves are guides for the eye); FIG. 7B is theequivalent distribution for particles' refractive indices with the arrowindicating redistribution of probabilities from a low density tail in astock sample to the peak in the coated sample; and

FIG. 8 shows a schematic block diagram of a computer system forimplementing the methods of the invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

A holographic microscope 100 constructed for implementation of theinvention is depicted schematically in FIG. 1A. Sample 110 isilluminated with the collimated and linearly polarized beam 120 from aHeNe laser operating at a vacuum wavelength of A=632.8 nm (Uniphase 5mW). Other laser wavelengths, such as 2=537 can also be employed(Coherent Verdi at 5 W). Light 130 scattered by the sample 110interferes with the unscattered portion of the illuminating beam 120 toform an in-line hologram in the focal or imaging plane 125 of themicroscope 100. The resulting heterodyne scattering pattern (see FIG.1C(1)) is magnified by the microscope's objective lens 145 (Zeiss S PlanApo 100× oil immersion, numerical aperture 1.4), and projected with a 1×video eyepiece onto a video camera 135 (or plural camera for someembodiments) (NEC TI-324AII), which records 1 ms exposures every 33 mswith a system magnification of 101 μm/pixel. As described hereinafterthis scattering, or interference pattern, is fit to predictions of theLorenz-Mie theory (see FIG. 1C(2)).

This video signal can be either recorded as an uncompressed digitalvideo stream at 30 frames/s on a commercial digital video recorder(Pioneer H520S) for off-line analysis, or digitized directly with anArvoo Picasso PCI-2SQ framegrabber to yield an eight-bit image, A(r).Normalizing each image by a previously recorded background image, B(r),eliminates spurious interference fringes due to reflections andimperfections in the optical train and provides the real-valued arraya(r)=a(r)/B(r) for analysis. In our implementation, each pixel in the640/480 array contains roughly five bits of information.

We interpret the data in a(r) using results for generalized Lorenz-Miescattering theory. The electric field in the microscope's focal plane isthe superposition of the incident plane wave,E₀(r)=u₀(x,y)exp(ikz){circumflex over (x)}, and the scattering patternE_(s)(r)=u₀(r_(p))f_(s)(k(r−r_(p))) due to a sphere centered at r_(p).There, k=2πn_(m)/λ is the light's wavenumber in a medium of refractiveindex n_(m). After normalization,

a(r)≈1+2

{exp(−ikz _(p))f _(s)(k(r−r _(p)))·{circumflex over (x)}}+|f _(s)(k(r−r_(p))².  (1)

The scattering function may be expanded in a series of vector sphericalharmonics

${{f_{s}({kr})} = {\sum\limits_{n = 1}^{n_{c}}{{fn}( {{{ia}_{n}{N_{e\; 1n}^{(3)}({kr})}} - {b_{n}{M_{o\; 1n}^{(3)}({kr})}}} )}}},$

where f_(n)=i^(n)(2n+1)/[n(n+1)]. The generalized Lorenz-Mie expansioncoefficients, a_(n) and b_(n), depend on the size, shape, compositionand orientation of the scattering particle in the illuminating field.For a homogeneous isotropic sphere of radius a illuminated by a planewave of wave number k, these coefficients fall off rapid with order n,and the series is found to converge after a number of termsn_(c)=(ka)+4.05(ka)^(1/3)+2. For a micrometer-scale latex sphere inwater, n_(c)≦30. The normalized image of an individual sphere can be fitto Eq. (1) for the sphere's position r_(p), its radius a, and itsrefractive index n_(m).

Although the scattering coefficients must be computed with great care[10, 11], the numerical challenge presented by Eq. (2) is in evaluatingthe vector spherical harmonics M_(o1n) ⁽³⁾(k(r−r_(p))) and N_(eln)⁽³⁾(k(r−r_(p)) at each pixel in a(r) for each trial value of r_(p). Eachsphere's image can subtend tens of thousands of pixels, and thefunctions typically must be evaluated hundreds of times in the course ofeach nonlinear fit. Even with the best conventional computationallyefficient formulations of the relevant special functions, a fullyconverged fit can take several seconds on a single processor.

One most preferred form of the invention concerns methods to acceleratethese fits using the Lorenz-Mie technique combined with particularprogramming steps. As will be shown hereinafter this methodology revealssolutions to problems and enables commercially effectivecharacterizations, wherein those solutions were not even previouslyavailable. One of our reference systems consists of micrometer-scalelatex spheres freely diffusing in water at room temperature, whosenormalized hologram is shown in FIG. 1C(1). We analyze images such asthis with software developed in the IDL programming language (ITT VisualInformation Solutions, Boulder, Colo.), taking advantage of the MPFITsuite of Levenberg-Marquardt nonlinear least-squares fitting routines.These fits typically yield the particle's in-plane position to within 3nm, its axial position to within 10 nm, its radius to within 1 nm andits refractive index to within 1 part in 10⁴. Error estimates obtainedfrom uncertainties in the fit parameters are independently confirmed bydynamical measurements.

Much of the computational burden of fitting Eq. (1) to a normalizedholographic image can be relieved by evaluating f_(s)(kR) along the linesegment R=|r−r_(p)| and then interpolating to obtain f_(s)(k(r−r_(p))).This approach exploits the approximate radial symmetry of a(r) about theparticle's center. The data in FIG. 2 demonstrate the substantialreduction in processing time attained in this way. Although expedient,one-dimensional look-up tables do not account for slightpolarization-dependent asymmetries in spheres' image, and can fail tocapture rapidly varying features in a(r). Consequently, results for theparticle's position and characteristics obtained from interpolated fitsdiffer slightly from reference value obtained with two-dimensional fits.Under circumstances where precision can be sacrificed for speed, theconvergence tolerances on both one- and two-dimensional fits can berelaxed to obtain results with fewer optimization cycles. For instance,accepting tracking errors of 5 nm in plane and 20 nm in the axialdirection yields a tracking rate for a 201×201 pixel image of 2 frames/son a 3.2 GHz Intel Core 2 Duo processor, as shown in FIG. 2.

More substantial gains can be obtained by combining the Lorenz-Mieformalism with exploiting the parallel processing capabilities of agraphical processing unit (GPU) typically used in high-end computergraphics cards. Further detail concerning the GPU will be illustratedherinafter in reference to FIG. 8 and the computer 200. Whereasconventional CPU-based implementations operate on each pixel insequence, a GPU-enabled algorithm operates on all pixels simultaneously.We implemented a GPU-enabled computation of f_(s)(kr) using the GPUlib(Tech-X Corp., Boulder, Colo.) extensions to IDL on an nVidia 280 GTXgraphics card (nVidia Corp., Santa Clara, Calif.) installed in the hostcomputer. GPUlib provides access to the underlying CUDA framework formathematical computation on GPUs without requiring the sophisticatedprogramming techniques typically required to implement mathematicalcomputations on GPUs. With these enhancements, two-dimensional fits runwith full precision at nearly 3 frames/s, a factor of 20 faster thanCPU-based analysis. Accepting 5 nm in-plane resolution and 50 nm axialresolution yields particle tracking and characterization data at morethan 5 frames/s, as shown in FIG. 2. The GPU, furthermore, supportsmulti-threaded operation. When supported by a multi-core CPU, this meansthat several analyses can proceed in parallel, yielding a proportionalincrease in total processing speed. This may be considered to bereal-time performance in some applications. The meaning of “real time”is that image data from each frame snapshot of image data is availablefor processing and use before the net frame snapshot arrives. As will benoted hereinafter this allows real time characterization of a particleof a sample, such as for example, of a sample's position, radius andindex of refraction, and molecular level coatings like bead basedmolecular binding features. At least two of these parameters can bedetermined at a time and can even be all simultaneously. Substantialfurther acceleration could be attained by implementing the same fittingalgorithm in an optimized compiled programming language.

Even if fitting to a particle's image proceeds rapidly enough forreal-time applications, analyzing a snapshot requires a preliminaryidentification of the particles of the sample 110 in the field of view,and starting estimates for the particle's position, size and refractiveindex that are sufficiently accurate for the fit to converge to theglobally optimal solution. This bootstrapping process must be both fastand reliable if holographic analysis is to be useful for unattendedautomated processing.

Each sphere appears in a snapshot, such as the example in FIG. 3A, asconcentric bright and dark rings. The gradient of the intensity at eachpixel therefore defines a line segment in the imaging plane along whicha sphere's center may lie. The intersection of such lines defines anestimate for the particle's centroid in the focal plane. In the mostpreferred embodiment the particle is a sphere. We identify suchintersections with a simplified variant of the circular Hough transformin which each pixel in the original image casts “votes” for the pixelsin the transformed image that might be centroids. FIG. 3A indicates thevotes cast by three representative pixels in the original image. Thesingle-pixel votes are accumulated in a transformed image, such as theexample in FIG. 3B. In this case, the transformed image has the sameresolution as the original, a choice that yields both reasonableaccuracy and speed. Those pixels in the transformed image with the mostvotes are taken to be centroid candidates, and their locations used asthe in-plane coordinates to initialize fits. The inset surface plotsdemonstrate how the extended interference pattern due to a single sphereis transformed into a sharply defined peak, even if two or more spheres'holographic images overlap. This methodology is more computationallyefficient than the conventional circular Hough transform, which usesadditional resources to record information about each potential circularregion's radius. Refining the centroid estimate by computing thebrightness-weighted center of brightness for each feature in thetransformed image typically identifies particles' centroids to within afew tenths of a pixel, or a few tens of nanometers.

Having estimated a particle, or sphere's, in-plane coordinates, we thenestimate its axial coordinate by back-propagating the measured lightfield using the Rayleigh-Sommerfeld propagator. Peaks in thereconstructed axial intensity correspond with particle positions towithin 100 nm, even when particles occlude each other along the opticalaxis. This back-propagation can be performed with a one-dimensionalslice of image data, centered on the particle's position, and thereforecan be performed very rapidly.

Accurately estimating the size and refractive index of an unknownparticle is substantially more difficult. Fortunately, the error surfacefor the nonlinear fits slopes smoothly and monotonically toward theglobally optimal values over a very large catchment basin in theparameter space defined by a_(p), n_(p), and z_(p). FIG. 4 shows theroot-mean-square error in the local image intensity computed for a 1.5mm diameter silica sphere in water at z_(p)=20 mm, as a function ofΔa_(p), Δn_(p) and Δz_(p) errors in the radius, refractive index andaxial position of the particle, respectively. These data demonstratethat fits to such a particle's image should converge to the optimalvalues even if the initial estimates are in error by more than 0.1 inthe refractive index, 0.5 mm in the radius and 2 mm in the axialposition. The error surface becomes more highly structured, and thusless forgiving, if the estimated in-plane centroid is in error by morethan a hundred nanometers or so. Fortunately, the voting algorithmroutinely yields sufficiently accurate results to ensure robustconvergence. Tracking a particle through a sequence of images can befurther accelerated by using the results from one fit as the initialestimates for the next. In this case, no additional pre-fitting isrequired.

The combination of rapid centroid identification and accelerated imagefitting yields accurate and highly precise measurements of colloidalspheres' positions and characteristics in near or in real time asdescribed hereinbefore. Unattended holographic particle tracking andcharacterization should find numerous applications in process controland quality assurance as well as in high-throughput and combinatorialassays. Substantial further acceleration should be possible through moreaggressive software optimization and parallelization, without recourseto exotic hardware solutions.

Holographic particle tracking has immediate applications forthree-dimensional particle image velocimetry. FIG. 5A shows an examplein the form of the superimposed trajectories of 500 individual onemicrometer-diameter polystyrene spheres (Duke Scientific, catalog number5100A) travelling down a 2 cm long microfluidic channel of 100 μm widthand 17 μm depth. The spheres were dispersed in water at a volumefraction of 10-⁵, and were advected by a pressure-driven flow of watercreated by raising a reservoir against gravity. Images were obtained ina 50×70 μm² area near the middle of the channel, with the focal planeset roughly 5 μm below the lower glass/water interface. Spheres'locations in each snapshot are linked with a maximum-likelihoodformalism approach into single-particle trajectories, r_(p)(t), sampledat 1/60 s intervals. Not every time step is represented in eachparticle's trace because faster-moving particles near the mid-plane ofthe flow occasionally obscure slower-moving particles near the walls.FIG. 5A presents only those particle positions that were identifiedunambiguously. Even such incomplete time series can be used to estimatethe particles' instantaneous velocities. The traces in FIG. 5A are of agray scale according to the trajectory-averaged speed.

These trajectories also are useful for mapping the three-dimensionalflow field. Each point in FIG. 5B represents one particle's speed as afunction of its mean height, z, in the microfluidic channel. Thesuperimposed results of 1000 such trajectories clearly show theparabolic flow profile expected for Poiseuille flow down a channel, thewidth of the cluster of data reflecting spatial variations across thelong horizontal axis of the channel. The limits of the vertical axisindicate the positions of the channel's upper and lower walls, withheights being reported relative to the microscope's focal plane. Thedashed horizontal lines represent the region of the flow into whichparticles cannot wander because of their hard-sphere interaction withthe glass walls. The fit parabola shows the flow vanishing at thechannel's boundaries.

Each trajectory also yields trajectory-averaged measurements of theradius and refractive index for each particle individually. Combiningmultiple measurements on a single particle minimizes systematic errorsdue to inevitable position-dependent variations in the illumination. Theresults in FIG. 6A(1)-A(3) show the radii and refractive indexes of thespheres in a commercial sample of polystyrene microspheres dispersed inwater. FIGS. 6A(2) and A(3) show the 2D histograms taken from FIG.6A(1). The mean radius of a_(p)=0.4995 μm agrees with the manufacturer'sspecification obtained by conventional light scattering, as does themeasured 2.5 percent polydispersity in the radius. The mean refractiveindex of n_(p)=1.595 is consistent with independent measurements onpolystyrene spheres.

Single-particle characterization is a substantial benefit of holographiccharacterization compared with bulk light-scattering measurements, whichare the usual basis for analyzing particle dispersions. Building updistributions such as the example in FIGS. 6A(1)-A(3) fromsingle-particle measurements eliminates the need for population models,and thus affords more general insights into a sample's composition. Forexample, the anticorrelation between the particles' size and refractiveindex evident in FIGS. 6A(1)-A(3) would not be apparent in lightscattering data. No such anticorrelation is apparent in holographicanalyses of homogeneous fluid droplets. One interpretation of thisobservation is that the larger spheres in the emulsion polymerizedsample are more porous, and consequently have lower refractive indexes.

Simultaneously tracking and characterizing individual particles (and inreal time as described hereinbefore) enables us to confirm our results'freedom from motion-based artifacts. Colloidal particles' images becomeblurred if they move during the period that the camera's shutter isopen. This blurring introduces substantial artifacts into conventionalbright-field video microscopy data. As the results in FIGS. 6B(1) andB(2) demonstrate, however, motion blurring has no discernible influenceon values for the radii and refractive indexes as a function of meanspeed obtained by holographic analysis for speeds as high as 500 μm/s.Additional measurements reveal deviations from the population averagevalues only for peak flow speeds exceeding 700 μm/s.

This robustness is surprising because particles travelling at severalhundred micrometers per second traverse several of our camera's pixelsduring its 1 ms shutter period. The resulting incoherent average of theoscillatory scattering pattern serves primarily to reduce the contrastin the direction of motion, however, and so has little influence on theLorenz-Mie fit. Even this amount of blurring could be reduced throughthe use of a faster shutter or a pulsed laser for illumination.

Being able to characterize individual colloidal particles in real timeas they travel down a microfluidic channel provides an effective basisfor detecting molecular-scale coatings on functionalized beads. If theindividual spheres' radii were known to within a nanometer or so, thenthe presence of a molecular coating of similar refractive index could bediscerned in the apparent increase in the radius. More generally, thecharacteristics of a treated sample can be compared with controlmeasurements on untreated spheres.

FIGS. 7(A) and 7(B) shows one such comparative example study of 2 μmdiameter biotinylated polystyrene spheres before and after incubationwith neutravidin. The biotinylated polystyrene spheres used in thisstudy were obtained from Polysciences Inc (Warrington, Pa.) (catalognumber 24172). Neutravidin was obtained from Invitrogen (Carlsbad,Calif.) (catalog number A2666). A neutravidin solution at aconcentration of 1 mg/mL was prepared by adding 1 mg of neutravidin to 1mL of phosphate buffer saline (PBS) (50 mM, [NaCl]=50 mM). The stocksample of beads was obtained by adding 10 μL of the as-delivereddispersion to 990 μL of PBS. The coated sample was prepared by adding 10μL of the as-delivered dispersion to 990 μL of neutravidin solution.Particles were incubated and shaken at room temperature for 1 hr beforethey were introduced into the microfluidic channels by capillary action.Flow was induced by introducing a slip of absorbent paper into one endof the channel and images recorded until results were obtained for 1,000spheres from each sample. Each data set consisted of roughly 5,000holographic measurements, which were obtained over the course of roughly5 min.

From these measurements, we determined that the untreated sample has apopulation averaged radius of 0:996±0:015 μm (see FIG. 7A), consistentwith the manufacturer's specification. The incubated population appearsto some 6 nm larger, with an average radius of 1:002±0:015 μm. Eventhough the two size distributions plotted in FIG. 7A overlapsubstantially, a Wilcoxon rank-sum test demonstrates that their meansdiffer with better than 99 percent certainty. This then constitutes astatistically significant detection of change in the treated sample'sradius, which can reasonably be ascribed to the presence of amolecular-scale coating. The coating's thickness, in this case, isconsistent with the size of a multi-domain avidin derivative.

Pronounced differences between the two samples also are evident in themeasured distribution of refractive indexes, plotted in FIG. 7B. Theincubated sample's distribution is significantly sharper, presumablybecause protein, whose refractive index is similar to that ofpolystyrene, displaces water in the spheres' porous surfaces, and raisestheir effective refractive indexes. This would affect the more porousparticles on the lower side of the refractive index distribution morethan the denser particles on the high side, thereby sharpening thedistribution. The arrow in FIG. 7B indicates this redistribution.

Similar analyses of random samples of the two data sets further confirmthat the particles from the untreated sample all come from the samepopulation, whose size and refractive index is consistent with themanufacturer's specification. The treated samples, by contrast show morevariability in size, possibly because the thickness and evenness of thebound avidin layer can vary from sphere to sphere.

These results demonstrate the utility of hardware-accelerated digitalvideo microscopy for detecting in real time molecular-scale coatings onfunctionalized colloidal spheres. Unlike conventional molecular bindingassays, holographic analysis does not require fluorescent orradiological markers, and so eliminates the effort and expenseordinarily required to label molecules bound to beads.

In one embodiment of the invention the method of the invention can beimplemented to determine parameters and features of interest by use ofthe computer system shown in FIG. 8. The system of FIG. 8 includes acomputer 200 (which can include a CPU and/or GPU in a most preferredembodiment as described herein in connection with Lorenz-Mie analysis)which can execute a computer readable medium, such as a computersoftware module with instructions which are embedded, for example, in acomputer addressable storage medium 210. The use of the GPU in thecomputer 200 thereby allows real time analysis and simultaneousevaluation of parameters such as molecular coatings and/or of aparticle's position, radius and index of refraction. This storage medium210 can be read/writeable which enables data to be written thereto. Thisfeature allows subsequent static or dynamic data analysis; and resultsof that analysis allow a user to act on that information foradvantageous applications. The computer 200 executes the computersoftware module instructions to analyze data produced by the previouslydescribed methods of the invention. Such data can be obtained from thestorage medium 210 and input via device 220. Other conventional devices,such as an output device 230 (e.g., a display, printer and/or a storagemedium) can enable viewing and further data analysis. Such analysis canyield information about the position and characteristics of particles inreal time or delayed time.

Certain embodiments described hereinbefore use holographic videomicroscopy in a single wavelength to detect molecular-scale coatings onmicrometer-diameter dielectric colloidal spheres. This detection wasaccomplished by analyzing a population of spheres that had been exposedto the coating molecules and comparing the results with those obtainedby analyzing a comparable population of spheres that had not beenexposed. Holographic snapshots of individual spheres in each populationwere analyzed with the Lorenz-Mie theory of light scattering to obtainestimates for the sphere's radius and complex refractive index.Lorenz-Mie analysis yields each sphere's radius with nanometerresolution and its refractive index to within a part in a thousand. Thesystematic differences in the population distributions of theseproperties constitute the basis for detecting the molecules. Coatedspheres appear systematically larger by an amount consistent with thethickness of the coating.

In an alternative embodiment, the Lorenz-Mie analysis can employtwo-color or multi-color holograms to provide comparable detectionresolution using only a single sphere, rather than populations ofspheres. Thus the input beam 120 in FIG. 1A provides an output of amulti-color hologram. This embodiment creates simultaneous holographicimages in two or more wavelengths. These multi-color holograms can berecorded on separate video cameras 135 (see FIG. 1A) using filters toseparate the images. Alternatively, they can be recorded with a colorcamera 135, and the separate images obtained from the recorded colorchannels.

The spheres used for these types of measurements should have comparableoptical properties in the wavelengths used. The coating, however, shouldhave strongly differing properties in at least two of the wavelengths.For instance, the coating might be a pure dielectric in one wavelengthand strongly absorbing in another. In the absence of a coating,holograms obtained in multiple wavelengths should yield identicalresults for the particle's position and size. Coated spheres' hologramsshould differ significantly in the estimated size and in the qualitativefeatures of the estimated refractive index obtained from eachwavelength. Such differences would constitute a detection of themolecular-scale coating. Suitable choice of wavelength, sphere size andsphere composition should provide quantitative information on thethickness or completeness of the coating.

The foregoing description of embodiments of the invention has beenpresented for purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdisclosed, and modifications and variations are possible in light of theabove teachings or may be acquired from practice of the invention. Theembodiments were chosen and described in order to explain the principalsof the invention and its practical application to enable one skilled inthe art to utilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated.

What is claimed is:
 1. A method of characterizing a parameter of asample by holographic microscopy, comprising the steps of: receivingmulticolor holographic image data of the sample from a storage medium;determining a first estimate of the number of objects in the holographicimage data, each object associated with a set of concentric bright anddark rings; determining, for each set of concentric bright and darkrings, by a voting algorithm, a centroid defined by an approximate x, yposition in a plane, with each pixel of the image data voting for pixelsin a transformed image that may be centroids; determining an estimate ofthe axial position (z) of each of the objects; determining by Lorenz-Mieanalysis an estimate of each of the objects' radius, refractive index;using holographic image data from the sample to characterize propertiesof the sample and generate information characteristic of the parametersof the sample; and comparing the holographic image data with controlholographic image data corresponding to an uncoated sample anddetermining if the sample has a coating.
 2. The method as described inclaim 1 wherein the step of providing the image data includes generatingmultiple beams of polarized light, each of the multiple beams having adifferent wavelengths and scattering each of the multiple beams off thesample, to generate the multi-color hologram data.
 3. The method ofclaim 1, further comprising analyzing the information characteristic ofthe sample parameters and determining in real time simultaneously size,position and refractive index of a particle of the sample.
 4. The methodas defined in claim 1 wherein an associated plurality of holograms areformed by interaction between the sample and the plurality ofwavelengths of coherent light, thereby enabling determination ofdifferent responses of the sample to the different wavelengths ofcoherent light and analyzing the different response to identify theparameters of the sample.
 5. The method as defined in claim 1 whereindetermining the centroid further includes determining the Lorenz-Miefunctionality scattering function f_(s)(kr) along a line segmentR=|r−r_(p)| and interpolating to obtain a function f_(s)(k(r−r_(p)))thereby reducing processing time and providing real time analysis of thesample.
 6. The method as defined in claim 1 further including the stepsof performing the Lorenz-Mie analysis and obtaining comparisons betweenof the image data a particle being in an untreated state and anotherparticle having undergone a treatment, thereby enabling real timecharacterization of molecular layers present on the treated particleversus the untreated particle.
 7. The method as defined in claim 6wherein the real time characteristics are selected from the group ofindex of refraction and particle radius.
 8. The method as defined inclaim 1 further including the step of estimating in-plane co-ordinatesof the particle by the Lorenz-Mie analysis and then estimating axialcoordinate of the particle by back-propagating the measured light fieldapplying a Rayleigh-Sommerfeld propagator.
 9. The method as defined inclaim 1 wherein the analysis step includes applying aLevenburg-Marquardt fitting routine to identify the in-plane co-ordinatewithin 3 nm.
 10. The method as defined in claim 1 further including thesteps of determining velocity of the particle in a flowing form.
 11. Themethod as defined in claim 10 further including the step of mapping athree-dimensional flow field of the particle.
 12. The method as definedin claim 10 wherein the step of analyzing the information comprisessimultaneously tracking and characterizing individual ones of theparticles, thereby avoiding motion induced artifacts of thecharacteristics of the particles.
 13. The method as defined in claim 1wherein the step of measuring includes identifying molecular-scalecoatings on functionalized forms of the particle by detecting variationsin apparent increase in radius.
 14. A system for characterizing aparameter of a sample by holographic microscopy, comprising: aholographic microscope including a laser beam source and an objectivelens, the laser beam scattering from the sample and interacting with anunscattered portion of the laser beam to provide a holographicscattering pattern, an image collection device for collecting image datacharacteristic of the scattering pattern from the holographicmicroscope; and, a computer system including a processor and memory, thememory having stored thereon computer readable instructions, thecomputer readable instructions configured to: computer software which isexecuted by the computer to analyze the image data, the computersoftware including a Lorenz-Mie methodology and which is executed by agraphical processing unit to provide substantially real time output ofparameters characteristic of the sample. receiving holographic imagedata of the sample; determining a first estimate of the number ofobjects in the holographic image data, each object associated with a setof concentric bright and dark rings; determining, for each set ofconcentric bright and dark rings, by a voting algorithm, a centroiddefined by an approximate x, y position in a plane, with each pixel ofthe image data voting for pixels in a transformed image that may becentroids; determining an estimate of the axial position (z) of each ofthe objects; determining by Lorenz-Mie analysis an estimate of each ofthe objects' radius and refractive index; comparing one of the radiusand refractive index for each of the objects the same of radius orrefractive index of a control uncoated sample; and determining for eachone of the objects if that one object is coated.
 15. The system of claim14, wherein the holographic microscope includes a plurality of laserbeams corresponding to multiple wavelengths and wherein the computerreadable memory is configured to receive multi-color holographic imagedata.
 16. The method as described in claim 15 wherein each of theplurality of laser beams are configured to engage a microfluidic channelhaving the plurality of particles.
 17. A method of characterizingparameters for holographic microscopy of objects comprising the stepsof: receiving image data from a storage medium; transforming the imagedata using a Hough circular transform to determine by a voting algorithma first estimate of the number of objects in the image data and theobjects approximate x, y position in a plane; applying Lorenz-Mieanalysis of the image data for each of the objects to determine anestimate of the radius and refractive index of each of the objects;identifying from one or both of estimated radii and estimated refractiveindices those particles having a coating.
 18. The method of claim 17,wherein the determination of a centroid is by application of a circularHough transformation wherein each pixel in an original image votes forthe pixels in a transformed image.